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Use the table to answer the question.

x y
0 −5
1 −9
2 −13
3 −17
Which of the following equations correctly describes the function in the table using function notation?
Responses:

f(x)=−5x−4

f(y)=−5x−4

f(y)=−4x−5

f(x)=−4x−5

5 answers

To find the function that describes the data in the table, we can analyze the given points (x, y):

  • (0, -5)
  • (1, -9)
  • (2, -13)
  • (3, -17)

Next, we determine how y changes in relation to x. Looking at the differences in the y-values:

  • From x = 0 to x = 1: -5 to -9 (decrease by 4)
  • From x = 1 to x = 2: -9 to -13 (decrease by 4)
  • From x = 2 to x = 3: -13 to -17 (decrease by 4)

This indicates a linear relationship with a constant decrease of 4 for every increase of 1 in x.

Now we can find the slope (m) of the line, which is -4, and we can use the point-slope form of a linear equation. We start with the formula:

\[ y = mx + b \]

Substituting in the values we've found:

\[ y = -4x + b \]

To find b (the y-intercept), we can use one of the points from the table. Let's use (0, -5):

\[ -5 = -4(0) + b \] \[ b = -5 \]

So, the equation that describes the function is:

\[ y = -4x - 5 \]

Using function notation, we write this as:

\[ f(x) = -4x - 5 \]

Thus, the correct answer is:

f(x) = -4x - 5

The function V(r)=10πr^2 represents the volume of a cylinder that is 10 inches high with a radius of r. Which is the correct interpretation for the function notation V(3)=90π ?(1 point)
Responses

A radius of 3 gives the value 90.

The volume of the cylinder is 3 when the radius is 90π.

A cylinder of 90π is produced from a radius of 3.

The volume of the cylinder is 90π when the radius is 3.

To interpret the function notation \( V(3) = 90\pi \) correctly, we need to understand that \( V(r) = 10\pi r^2 \) gives us the volume of a cylinder based on its radius \( r \).

When we substitute \( r = 3 \) into the function, we calculate the volume associated with that radius:

\[ V(3) = 10\pi(3^2) = 10\pi(9) = 90\pi \]

Thus, \( V(3) = 90\pi \) means that the volume of the cylinder is \( 90\pi \) cubic inches when the radius is 3 inches.

Given this understanding, the correct interpretation of \( V(3) = 90\pi \) is:

The volume of the cylinder is \( 90\pi \) when the radius is 3.

Monique is punting a football and the height the ball travels is a function of time. The function h(s)=−s^2+10s+3 gives the height of the ball, h(s) , given the number of seconds, s , that the ball has been in the air. After flying through the air for 7.5 seconds, what is the height of the ball? Find h(7.5) .
Responses:

21.5

24

134.25

21.75

To find the height of the ball after flying through the air for \( s = 7.5 \) seconds, we need to evaluate the function \( h(s) = -s^2 + 10s + 3 \) at \( s = 7.5 \).

Let's substitute \( s = 7.5 \) into the function:

\[ h(7.5) = - (7.5)^2 + 10(7.5) + 3 \]

First, calculate \( (7.5)^2 \):

\[ (7.5)^2 = 56.25 \]

Now substitute this value back into the function:

\[ h(7.5) = -56.25 + 10(7.5) + 3 \]

Now calculate \( 10(7.5) \):

\[ 10(7.5) = 75 \]

So, we can now rewrite \( h(7.5) \):

\[ h(7.5) = -56.25 + 75 + 3 \]

Now calculate \( -56.25 + 75 \):

\[ -56.25 + 75 = 18.75 \]

Now add 3:

\[ 18.75 + 3 = 21.75 \]

Thus, the height of the ball after 7.5 seconds is:

\[ \boxed{21.75} \]